Question

Two identical capacitors $A$ and $B$, charged to the same potential $5V$ are connected in two different circuits as shown below at time $t = 0$. If the charge on capacitors $A$ and $B$ at time $t = CR$ is $Q_A$ and $Q_B$ respectively, then (Here e is the base of natural logarithm)

• A. $Q_{A}=VC, Q_{B}=CV$
• B. $Q_{A}=\frac{CV}{2}, Q_{B}=\frac{VC}{e}$
• C. $Q_{A}=\frac{VC}{e}, Q_{B}=\frac{CV}{2}$
• D. $Q_{A}=VC, Q_{B}=\frac{VC}{e}$

Answer 1

Answer: (D)

$Q_{A}=VC, Q_{B}=\frac{VC}{e}$

Answer 2

For (A)
No current flows
Hence $Q_A = CV$
For (B)
$i = \frac{V}{R}e^{-\frac{t}{RC}}$
$q = CV e^{\frac{t}{RC}}$
$Q_{B} = CVe^{-1} = \frac{CV}{e}$